Recent questions in 2000

During an adiabatic process, if the pressure of an ideal gas is proportional to the cube of its temperature the ratio $\gamma = \frac{c_p}{c_v}$ is : <br> (Specific heat at constant volume = $c_v$ <br> specific heat at constant pressure = $c_p$ )

asked Dec 19, 2018 by pady_1

0 answers

The area of the triangle formed by the axes and the line $(\cos \alpha - \sin \alpha ) x + (\cos \alpha + \sin \alpha) y =2$ , in square units, is :

asked Dec 19, 2018 by pady_1

0 answers

The co-ordinate of the image of the origin $O$ with respect to the straight line $x+y+1=0$ is:

asked Dec 19, 2018 by pady_1

0 answers

If the points $(1,2)$ and $(3,4)$ were to be on the same side of the line $3x -5y +a =0$ , then:

asked Dec 19, 2018 by pady_1

0 answers

If the point $[x_1 + t(x_2 - x_1), y_1 + t(y_2-y_1)]$ divides the join of the $(x_1,y_1)$ and $(x_2,y_2)$ internally, then :

asked Dec 19, 2018 by pady_1

0 answers

The vertices of a triangle are $(6,6), (0,6)$ and $(6,0)$ the distance between its circumcentre and centroid is :

asked Dec 19, 2018 by pady_1

0 answers

A straight rod of length 9 units slides with its ends. A and B always on the $x$ and $y$ axis respectively, then the locus of the centroid of $\Delta OAB$ is :

asked Dec 19, 2018 by pady_1

0 answers

If two towers of height $h_1$ and $h_2$ subtend angles $60^{\circ}$ and $30^{\circ}$ respectively at the mid point of the line joining their feet, then $h_1:h_2$ is equal to:

asked Dec 19, 2018 by pady_1

1 answer

In a $\Delta ABC, \; r_1 + r_2 - r_3 - r$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

In a $\Delta ABC, \; \cos A+ \cos B + \cos C$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If in a $\Delta ABC$ , $a,b,c$ are in AP then $\tan \frac{A}{2} \tan \frac{C}{2}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\cos x = \log_e (2 +\sqrt{3})$ , then $x$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\cos 2 + \sin 2$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\tan^{-1} 3 + \tan^{-1} n = \tan^{-1} 8$ , then $n$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\tan \theta + \sec \theta = \sqrt{3}$ , then the principal value of $\theta + \frac{\pi}{6}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\tan \theta_1 = k \cot \theta_2$ , then $\frac{\cos (\theta_1 - \theta_2)}{\cos (\theta_1 + \theta_2)}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\sin \alpha + \sin \beta = a, \; \cos \alpha + \cos \beta = b$ , then $\sin (\alpha + \beta) \cos^2 (\frac{\alpha - \beta}{2})$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\frac{\sin (-660^{\circ}) \tan (1050^{\circ}) \sec(-420^{\circ} )}{\cos(225^{\circ}) \mathrm{cosec} (315^{\circ}) \cos (510^{\circ})}$ is equal to:

asked Dec 19, 2018 by pady_1

0 answers

If $(\sin \alpha + \mathrm{cosec} \;\alpha)^2$ + $(\cos \alpha + \sec \alpha)^2$ = $k + \tan^2 \alpha + \cot^2 \alpha$ , then $k$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\frac{\cos A}{\cos B} = n , \; \frac{\sin A}{\sin B} = m$ , then $(m^2 - n^2) \sin^2B$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\begin{bmatrix} \frac{\sqrt{3} + 2 \cos A}{1- 2 \sin A} \end{bmatrix}^3 + \begin{bmatrix} \frac{1 + 2 \sin A}{\sqrt{3} - 2 \cos A} \end{bmatrix}^3$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The length of normal to the curve $y = \frac{1}{2} a(e^{x/a} + e^{-x/a})$ is :

asked Dec 19, 2018 by pady_1

0 answers

In the expression of $\begin{pmatrix} x^4 - \frac{1}{x^3} \end{pmatrix}^{15}$ coefficient of $x^{32}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $a \neq b, \; b, \; c$ satisfy $\begin{vmatrix} a & 2b & 2c \\ 3 & b & c \\ 4 & a & b \end{vmatrix} = 0$ then $b^2$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $d$ is the determinant of a square matrix $A$ of order $m$ , then the determinant of its adjoint, is :

asked Dec 19, 2018 by pady_1

0 answers

If $A=\begin{bmatrix} 1&3\\2&1 \end{bmatrix}$ , then the determinant of $A^2-2A$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $A$ and $B$ are two square matrices such that $B= -A^{-1}BA$ , then $(A+B)^2$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

$\begin{align}\frac{\frac{1}{2}. \frac{2}{2}}{1^3} + \frac{\frac{2}{2}. \frac{3}{2}}{1^3+2^3} + \frac{\frac{3}{2}.\frac{4}{2}}{1^3+2^3+3^3}+...+n \end{align}$ terms :

asked Dec 19, 2018 by pady_1

0 answers

Summation $\displaystyle\sum_{k=1}^{n} \;k \begin{bmatrix}1 +\frac{1}{n} \end{bmatrix}^{k-1}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The set $\{x \in R : x -2 + x^2 =0 \}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\alpha , \beta$ are the roots of the equation $9x^2+6x+1=0$ , then the equation with the roots are $\frac{1}{\alpha}$ , $\frac{1}{\beta}$ , is real to :

asked Dec 19, 2018 by pady_1

0 answers

The equation formed by decreasing each root of $ax^2+bx + c = 0$ by $1$ is $2x^2 + bx+ 2=0$ , then :

asked Dec 19, 2018 by pady_1

0 answers

If $3+i$ is a root of $x^2+ax+b=0$ , then $a$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

In the argand plane the area in square units of the triangle formed by the points $1+i, \; 1-i, \; 2i$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $1, \omega, \omega^2$ are the roots of unity, then $(a+b)^3 + (a \omega + b \omega^2)^3 + (a \omega^2 +b \omega)^3$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $\theta$ is real, the modulus of $\frac{1}{(1+\cos \theta) + i \sin \theta}$ is :

asked Dec 19, 2018 by pady_1

0 answers

The locus of the $z$ in the argand plane for which $|z+1|^2 + |z-1|^2 = 4$ , is a :

asked Dec 19, 2018 by pady_1

0 answers

If $\frac{n^2 +5}{(n^2+2)^2} = \frac{1}{(n^2+2) }+ \frac{k}{(n^2+2)^{2'}}$ then $k$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If the coefficient of $r^{th}$ term and $(r+1)^{th}$ term in the expansion of $(1+x)^{3n}$ are in the ratio $1 :2$ , then $r$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The coefficient of $x^{-n}$ in $(1+x)^n (1+\frac{1}{x})^n$ is :

asked Dec 19, 2018 by pady_1

0 answers

If $C_0, \; C_1, \; C_2, ....$ are binomial coefficients, then $C_1 + C_2 +C_3 + C_4 + ..... + C_r +.... + C_n$ is equal to:

asked Dec 19, 2018 by pady_1

0 answers

If $a_k = \frac{1}{k(k+1)}$ for $k = 1, 2, 3,...n$ , then $\begin{bmatrix} \displaystyle\sum_{k=1}^{n} a_k \end{bmatrix}^2$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

The number of quadratic expressions with the coefficient drawn from the set $\{0, 1, 2, 3\}$ is :

asked Dec 19, 2018 by pady_1

0 answers

The number of ways in which 13 gold coins can be distributed among three persons such that each one gets at least two gold coins is :

asked Dec 19, 2018 by pady_1

0 answers

If $^nC_3 : ^{n-1}C_4= 8:5$ , then $n$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $5^x = (0.5)^y = 1000$ , then $\frac{1}{x} - \frac{1}{y}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $x = \frac{2}{3 +\sqrt{7}}$ then $(x-3)^2$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $f : R \to R$ is defined by $g : R \to R$ are defined by $f(x) = 2x + 3$ and $g(x) = x^2 + 7$ , then the values of $x$ for which $f(g(x)) = 25$ , are :

asked Dec 19, 2018 by pady_1

0 answers

If $F : R \to R$ is defined by $f(x) = 2x + |x|$ then $f(2x) + f(-x) - f(x)$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

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